Questions tagged [integer]
For challenges involving the manipulation of integers.
411
questions
9
votes
3
answers
522
views
RADD decomposition of an integer
Introduction
The \$RADD(n)\$ operation is defined as the sum of \$n + [\$ the number whose decimal representation are the decimal digits of \$n\$ in reverse order \$]\$, see A004086. After reversal, ...
14
votes
4
answers
490
views
Find a matrix whose sliding sum is the input
Given a matrix like this:
1 1 3 -2
3 -4 1 -1
1 1 1 0
0 -1 0 0
By taking a 2×2 "sliding sum", where the sum of every 2×2 region of the matrix is ...
16
votes
11
answers
1k
views
Carryless factors
Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition:
...
19
votes
25
answers
1k
views
Carry-less sum given a base b
Given a list of positive integers \$\mathcal I=I_1,I_2,I_3,...,I_n\$ and a base \$b>1\$ return their "carry-less sum", i.e. represent \$\mathcal I\$ in base \$b\$ and sum digit-by-digit ...
1
vote
5
answers
210
views
Find number components with lowest distribution
Let us assume that we have number X.
Let us assume that we have positive integer "components" (C) of this ...
18
votes
9
answers
1k
views
Cryptic Multiplications
Given two non-negative integers e.g. 27, 96 their multiplication expression would be 27 x 96 = 2592.
If now each digits is ...
21
votes
44
answers
2k
views
Shifted auto-sum
Let’s take a positive integer such as 123. We define the shifted auto-sum of this integer as follows:
123 has 3 digits. We thus consider 3 copies of 123.
We stack ...
12
votes
6
answers
821
views
Exponential transform of an integer sequence
The exponential generating function (e.g.f.) of a sequence \$a_n\$ is defined as the formal power series \$f(x) = \sum_{n=0}^{\infty} \frac{a_n}{n!} x^n\$.
When \$a_0 = 0\$, we can apply the ...
24
votes
25
answers
3k
views
How far from binary?
Given a decimal integer n as input, output the smallest (in terms of absolute value) decimal integer m such that the absolute ...
10
votes
27
answers
2k
views
Find the nth Fibonacci number, where n is the mth Fibonacci number
Introduction
If \$\newcommand{\fib}{\operatorname{fib}}\fib(x)\$ calculates the \$x\$th Fibonacci number, write a program that calculates \$\fib(\fib(m))\$ for any integer value of \$m \ge 0\$. (Of ...
8
votes
5
answers
890
views
Spell out an integer... in NDos' way
Objective
Given a positive integer, spell it out in the conlang I made.
Specification
Let \$n\$ be the inputted integer. \$n\$ shall be spelled out in the following specification. The entire spelling ...
19
votes
6
answers
2k
views
Is it 1089-able?
\$ 1089 \$ is a very special number. To prove why, select any 3-digit number whose first and last digits differ by at least 2. Then, reverse the digits, and take the difference of these two numbers. ...
10
votes
11
answers
1k
views
13
votes
17
answers
1k
views
The interstice of two binary numbers
Given two integers, compute the two numbers that come from the blending the bits of the binary numbers of equal length(same number of digits, a number with less digits has zeros added), one after the ...
21
votes
26
answers
2k
views
Randomly Rounding
Input a decimal number and round it to an integer, randomly rounding up or down with a probability based on its fractional part, so the expected value of the output equals to the input value.
If ...
4
votes
19
answers
562
views
Double bit rotation to the right [closed]
Given a positive integer as input, output that integer, but with its bits rotated two times to the right. Also, think of the number as a donut of bits, eg. ...
12
votes
3
answers
284
views
Line Islands in a Word Search
My third word search related challenge in a row. :)
Challenge:
Brief explanation of what a word search is:
In a word search you'll be given a grid of letters and a list of words. The idea is to cross ...
4
votes
3
answers
266
views
Find All Digitroot Cyclic Sequences With Length Greater Than One
Digital sum, DR, Digit root is the iterative process of summing digits of a number until you end up with a single digit root number: e.g. digit root of 12345 is 6 since 1 + 2 + 3 + 4 + 5 = 15 = 1+5. ...
30
votes
17
answers
2k
views
How-many-bonacci-like is this sequence?
Inspired by @emanresu A's Is it a fibonacci-like sequence? Make sure to upvote that challenge as well!
We say a sequence is Fibonacci-like, if, starting from the third term (\$1\$-indexed), each term ...
10
votes
3
answers
312
views
Coordinates for a Heronian tetrahedron
Did you know that Heronian Tetrahedra Are Lattice Tetrahedra? A Heronian tetrahedron is a tetrahedron where
the length of each edge is an integer,
the area of each face is an integer, and
the volume ...
17
votes
28
answers
1k
views
Sum of the first n elements of the sequence of 9's complement
Let's consider the following sequence:
$$9,8,7,6,5,4,3,2,1,0,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71...$$
This is the sequence of \$9\$'s complement of a number: that is, \$ a(x) = 10^...
14
votes
15
answers
1k
views
How many blocks make a "truncated square-pyramid garden"?
A truncated square-pyramid of height \$h\$ has \$h\$ square layers where each layer has a side \$1\$ greater than the one above it, apart from the top layer which is a square of blocks with a given ...
31
votes
35
answers
3k
views
Is it a fibonacci-like sequence?
The Fibonacci Sequence is a sequence of positive integers where the first two elements are 1 and the rest are the sum of the previous two. It begins \$1, 1, 2, 3, 5, 8, 13\$ and continues forever.
But ...
21
votes
21
answers
1k
views
Is given number a concat of two squares
Given a positive integer, determine if it can be represented as a concatenation of two square numbers. Concatenated numbers may not begin with 0 (except for 0). Any leading zeros in input should be ...
17
votes
27
answers
2k
views
Prime a*b+c of N
Given an integer \$N\$, print or return integers \$a\$, \$b\$, and \$c\$ that satisfy all of the following conditions, if such integers exist:
\$a \times b + c = N\$
\$a\$, \$b\$, and \$c\$ are all ...
6
votes
1
answer
198
views
Represent any integer with an expression that uses no digit besides '4' [closed]
Fourward (Introduction)
I have an unhealthy obsession with the number 4. I love it so much, in fact, that seeing any other digit is frustrating to me. I therefour wish to create a 'Fourier ...
10
votes
6
answers
492
views
Mirror an integer... in NDos' way
NDos' Numeral System
NDos' numeral system is a numeral system invented by me. It represents every nonnegative integer by a binary tree. Given a nonnegative integer \$n\$:
If \$n=0\$, it is ...
16
votes
15
answers
1k
views
Encode integers with some others
Input a non-empty array of positive (greater than 0) integers. Output another non-empty array of positive integers which encode the input array. Output array does not use any numbers used in the input ...
25
votes
33
answers
2k
views
Even sum subarrays
Given an array of integers, count the number of contiguous subarrays with an even sum. You may assume that the array is non-empty, and contains only non-negative integers.
This is code-golf, so the ...
18
votes
6
answers
763
views
Is it an elementary matrix?
Consider a linear system of equations, in \$n\$ unknowns, expressed as
$$A \textbf x = \textbf b$$
where \$A \in M_{n,n}(\mathbb Z)\$ is an \$n \times n\$ matrix of integers, \$\textbf x\$ is a column ...
13
votes
9
answers
1k
views
Bijective meets mixed base
Background
A bijective base \$b\$ numeration, where \$b\$ is a positive integer, is a bijective positional notation that makes use of \$b\$ symbols with associated values of \$1,2,\cdots,b\$.
...
12
votes
2
answers
477
views
Branchless (MIPS) assembly code for median of 3
I was trying to write a short MIPS32 code for computing the median of three registers.
The rules:
Assume that some values are pre-loaded into $t0, ...
14
votes
12
answers
1k
views
Nega-Zeckendorf representation
Background
Zeckendorf representation is a numeral system where each digit has the value of Fibonacci numbers (1, 2, 3, 5, 8, 13, ...) and no two consecutive digits can be 1.
Nega-Zeckendorf ...
24
votes
18
answers
2k
views
Double trace of a square matrix
Inspired by a question (now closed) at Stack Overflow.
Given a square matrix, let its double trace be defined as the sum of the entries from its main diagonal and its anti-diagonal. These are marked ...
21
votes
9
answers
1k
views
Self-referential triangle sequence
Output the flattened version of the sequence A297359, which starts like the following:
...
29
votes
48
answers
3k
views
Swap Two Values in a List
Introduction:
Although we have a lot of challenges where swapping two items in a list is a subtask, like Single swaps of an array; Swap to Sort an Array; \$n\$ swaps into a nop; etc., we don't have ...
16
votes
7
answers
883
views
Maybe fractal sequence?
Background
A fractal sequence (Wikipedia; MathWorld) is an infinite sequence of positive integers meeting the following conditions:
Each positive integer appears infinitely many times in the sequence....
20
votes
12
answers
1k
views
Minimally prepend numbers to get a symmetric Young diagram
Background
A Young diagram is a diagram that represents a nonincreasing sequence of positive integers using left-justified rows of squares. As an example, 5, 4, 1 ...
24
votes
31
answers
3k
views
"-rot" transform
Background
-rot transform (read as "minus-rot transform") is a sequence transformation I just invented. This transform is done by viewing the sequence as a stack in Forth or Factor (first ...
12
votes
8
answers
1k
views
Boustrophedon transform
Related: Boustrophedonise, Output the Euler Numbers (Maybe a new golfing opportunity?)
Background
Boustrophedon transform (OEIS Wiki) is a kind of transformation on integer sequences. Given a sequence ...
18
votes
4
answers
625
views
Calculate the integer square root of a matrix
Let \$A\$ be a square matrix that is at least \$2 \times 2\$ where each element is an integer. \$A^2 = A \times A\$ will then have the same dimensions as \$A\$, and will have integer elements. For ...
5
votes
5
answers
232
views
Potential nonzero entries in an irregular sequence
Background
A338268 is a sequence related to a challenge by Peter Kagey. It defines a two-parameter function \$T(n,k)\$, which counts the number of integer sequences \$b_1, \cdots, b_t\$ where \$b_1 + \...
16
votes
19
answers
1k
views
Compare positions of integers in this sequence
A001057 is one way to represent an integer as a natural number. It lists them according to the following pattern:
0, 1, -1, 2, -2, 3, -3, 4, -4, ...
In this ...
15
votes
27
answers
3k
views
Make an array of random 128 bit integers
Given an input value \$n\$, construct an array of \$n\$ random 128 bit (unsigned) integers. The integers should be uniformly random.
Your code can use any in built random number generation function ...
8
votes
4
answers
329
views
Hexagonal section numbers
Introduction
Let's draw some regular hexagons formed by hexagonal tiles, marking the vertices of the tiles with dots. Then we will count the number of dots.
...
22
votes
22
answers
3k
views
Longest Zero Sum Sub-array
Given an array of integers. Find out its longest sub-array (contiguous subsequence) whose sum is 0.
The sub-array for output may be an empty array.
Input
Input an array of integers.
Output
Output the ...
5
votes
3
answers
160
views
Is this an ordinal transform? [duplicate]
Related: What's my telephone number? which asks to calculate the terms of A000085, the number of possible ordinal transforms of length n.
Background
Ordinal transform is a transformation on an integer ...
39
votes
15
answers
2k
views
Maximum number of squares touched by a line segment
Consider a square grid on the plane, with unit spacing. A line segment of integer length \$L\$ is dropped at an arbitrary position with arbitrary orientation. The segment is said to "touch" ...
32
votes
46
answers
3k
views
Is this a Permutation of 1..n
Input a non-empty array with \$n\$ positive integers. Test if the input array contains every integer in \$1\cdots n\$.
In case you prefer 0-indexed numbers, you may choose to input an array of non-...
27
votes
17
answers
3k
views
Give me odd, even, square, cube, prime and composite 3-digit numbers
Given a string which is guaranteed to be either odd, even, square, ...